Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Full text of review:
PDF
This review is available free of charge.
Book Information:
Authors:
Matthias Kreck and
Wolfgang Lück
Title:
The Novikov Conjecture: Geometry and algebra
Additional book information:
Oberwolfach Seminars, vol. 33, Birkhäuser-Verlag,
Basel,
2005,
xvi+ 267 pp.,
ISBN 3-7643-7141-2,
US$49.95$
Sylvain Cappell, Andrew Ranicki, and Jonathan Rosenberg (eds.), Surveys on surgery theory. Vol. 1, Annals of Mathematics Studies, vol. 145, Princeton University Press, Princeton, NJ, 2000. Papers dedicated to C. T. C. Wall. MR 1746325
Sylvain Cappell, Andrew Ranicki, and Jonathan Rosenberg (eds.), Surveys on surgery theory. Vol. 2, Annals of Mathematics Studies, vol. 149, Princeton University Press, Princeton, NJ, 2001. Papers dedicated to C. T. C. Wall. MR 1818769
Marshall M. Cohen, A course in simple-homotopy theory, Graduate Texts in Mathematics, Vol. 10, Springer-Verlag, New York-Berlin, 1973. MR 0362320
Steven C. Ferry, Andrew Ranicki, and Jonathan Rosenberg (eds.), Novikov conjectures, index theorems and rigidity. Vol. 1, London Mathematical Society Lecture Note Series, vol. 226, Cambridge University Press, Cambridge, 1995. Including papers from the conference held at the Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, September 6–10, 1993. MR 1388294
Steven C. Ferry, Andrew Ranicki, and Jonathan Rosenberg (eds.), Novikov conjectures, index theorems and rigidity. Vol. 2, London Mathematical Society Lecture Note Series, vol. 227, Cambridge University Press, Cambridge, 1995. Including papers from the conference held at the Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, September 6–10, 1993. MR 1388306
Eric M. Friedlander and Daniel R. Grayson (eds.), Handbook of $K$-theory. Vol. 1, 2, Springer-Verlag, Berlin, 2005. MR 2182598, DOI 10.1007/3-540-27855-9
Michel A. Kervaire and John W. Milnor, Groups of homotopy spheres. I, Ann. of Math. (2) 77 (1963), 504–537. MR 148075, DOI 10.1090/S0273-0979-2015-01504-1
John Milnor, On manifolds homeomorphic to the $7$-sphere, Ann. of Math. (2) 64 (1956), 399–405. MR 82103, DOI 10.2307/1969983
John Milnor, Lectures on the $h$-cobordism theorem, Princeton University Press, Princeton, N.J., 1965. Notes by L. Siebenmann and J. Sondow. MR 0190942
S. P. Novikov, Algebraic construction and properties of Hermitian analogs of $K$-theory over rings with involution from the viewpoint of Hamiltonian formalism. Applications to differential topology and the theory of characteristic classes. I. II, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 253–288; ibid. 34 (1970), 475–500 (Russian); English transl., Math. USSR-Izv. 4 (1970), 257–292; ibid. 4 (1970), 479–505. MR 0292913
A. A. Ranicki, Algebraic $L$-theory and topological manifolds, Cambridge Tracts in Mathematics, vol. 102, Cambridge University Press, Cambridge, 1992. MR 1211640
Andrew Ranicki, Exact sequences in the algebraic theory of surgery, Mathematical Notes, vol. 26, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1981. MR 620795
Andrew Ranicki, Algebraic and geometric surgery, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2002. Oxford Science Publications. MR 2061749, DOI 10.1093/acprof:oso/9780198509240.001.0001
Colin Patrick Rourke and Brian Joseph Sanderson, Introduction to piecewise-linear topology, Springer Study Edition, Springer-Verlag, Berlin-New York, 1982. Reprint. MR 665919
Stephen Smale, Generalized Poincaré’s conjecture in dimensions greater than four, Ann. of Math. (2) 74 (1961), 391–406. MR 137124, DOI 10.2307/1970239
C. T. C. Wall, Surgery on compact manifolds, 2nd ed., Mathematical Surveys and Monographs, vol. 69, American Mathematical Society, Providence, RI, 1999. Edited and with a foreword by A. A. Ranicki. MR 1687388, DOI 10.1090/surv/069
Shmuel Weinberger, The topological classification of stratified spaces, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1994. MR 1308714
- 1.
- Sylvain Cappell, Andrew Ranicki, and Jonathan Rosenberg (eds.), Surveys on surgery theory. Vol. 1, Annals of Mathematics Studies, vol. 145, Princeton University Press, Princeton, NJ, 2000; Papers dedicated to C. T. C. Wall. MR 1746325 (2000k:57004)
- 2.
- Sylvain Cappell, Andrew Ranicki, and Jonathan Rosenberg (eds.), Surveys on surgery theory. Vol. 2, Annals of Mathematics Studies, vol. 149, Princeton University Press, Princeton, NJ, 2001; Papers dedicated to C. T. C. Wall. MR 1818769 (2001i:57001)
- 3.
- Marshall M. Cohen, A course in simple-homotopy theory, Springer-Verlag, New York, 1973, Graduate Texts in Mathematics, Vol. 10. MR 0362320 (50:14762)
- 4.
- Steven C. Ferry, Andrew Ranicki, and Jonathan Rosenberg (eds.), Novikov conjectures, index theorems and rigidity. Vol. 1, London Mathematical Society Lecture Note Series, vol. 226, Cambridge University Press, Cambridge, 1995, Including papers from the conference held at the Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, September 6-10, 1993. MR 1388294 (96m:57002)
- 5.
- Steven C. Ferry, Andrew Ranicki, and Jonathan Rosenberg (eds.), Novikov conjectures, index theorems and rigidity. Vol. 2, London Mathematical Society Lecture Note Series, vol. 227, Cambridge University Press, Cambridge, 1995, Including papers from the conference held at the Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, September 6-10, 1993. MR 1388306 (96m:57003)
- 6.
- Eric M. Friedlander and Daniel R. Grayson (eds.), Handbook of
-theory, Springer-Verlag, Berlin, 2005, 2 volumes. MR 2182598 (2006e:19001)
- 7.
- Michel A. Kervaire and John W. Milnor, Groups of homotopy spheres. I, Ann. of Math. (2) 77 (1963), 504-537. MR 0148075 (26:5584)
- 8.
- John Milnor, On manifolds homeomorphic to the
-sphere, Ann. of Math. (2) 64 (1956), 399-405. MR 0082103 (18:498d)
- 9.
- -, Lectures on the
-cobordism theorem, Notes by L. Siebenmann and J. Sondow, Princeton University Press, Princeton, NJ, 1965. MR 0190942 (32:8352)
- 10.
- S. P. Novikov, Algebraic construction and properties of Hermitian analogs of
-theory over rings with involution from the viewpoint of Hamiltonian formalism. Applications to differential topology and the theory of characteristic classes. I. II, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 253-288; ibid. 34 (1970), 475-500, English translation, Math. USSR-Izv. 4 (1970), 257-292, 479-505. MR 0292913 (45:1994)
- 11.
- A. A. Ranicki, Algebraic
-theory and topological manifolds, Cambridge Tracts in Mathematics, vol. 102, Cambridge University Press, Cambridge, 1992. MR 1211640 (94i:57051)
- 12.
- Andrew Ranicki, Exact sequences in the algebraic theory of surgery, Mathematical Notes, vol. 26, Princeton University Press, Princeton, NJ, 1981. MR 620795 (82h:57027)
- 13.
- -, Algebraic and geometric surgery, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, Oxford, 2002, Oxford Science Publications. MR 2061749 (2005e:57075)
- 14.
- Colin Patrick Rourke and Brian Joseph Sanderson, Introduction to piecewise-linear topology, Springer Study Edition, Springer-Verlag, Berlin, 1982, Reprint. MR 665919 (83g:57009)
- 15.
- Stephen Smale, Generalized Poincaré's conjecture in dimensions greater than four, Ann. of Math. (2) 74 (1961), 391-406. MR 0137124 (25:580)
- 16.
- C. T. C. Wall, Surgery on compact manifolds, second ed., Mathematical Surveys and Monographs, vol. 69, American Mathematical Society, Providence, RI, 1999, edited and with a foreword by A. A. Ranicki. MR 1687388 (2000a:57089)
- 17.
- Shmuel Weinberger, The topological classification of stratified spaces, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1994. MR 1308714 (96b:57024)
Review Information:
Reviewer:
Jonathan Rosenberg
Affiliation:
University of Maryland, College Park
Email:
jmr@math.umd.edu
Journal:
Bull. Amer. Math. Soc.
43 (2006), 599-604
Published electronically:
July 28, 2006
Review copyright:
© Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
